Considering we are searching in the US, the scope could be
c=US,dc=acme,dc=com, we will limit the search in this branch. This is
done by adding internally a new assertion in the filter :

(&(ou=java)(ou=engineering)(scope.subtree="c=US,dc=acme,dc=com"))

<note>
This is not exactly how it is done in the server, it's just a 10K feet
presentation of the principles
</note>

You're on target yeah we add this node to the AST. BTW with alias dereferencing while searching the number of search bases expand in the scope node as we encounter aliases which "expand" the search space. Still we add one scope node but that scope node performs multiple assertions.

Now, the search engine do a computation on this filter to determinate
which index should be used. Suppose that the ou=java links to 10000
persons, and that the ou=engineering links to 1000 persons, we will use
the ou=engineering attribute to limit the number of candidate to bring
back from the backend, and check with the two other assertions to
eliminate the bad candidates. We do that by enumerating the number of
elements associated with eac assertion :

Yep this "annotation" of the modified filter AST is done by the optimizer. And BTW we'll be adding a new index which will give us an exact count for the scope node so we don't have to use MAX_INT anymore.

Currently, the scope assertion is just used to eliminate the candidates
which are found by the search engine, we don't 'count' the number of
candidates under a position on the tree (so the MAX_INT value). In our
sample, if we suppose that the scope is containing 100 entries, we
immediatly see that we are not using the correct assertion to bring back
the entries from the backend.

Right this will change. I will split the current hierarchy index (a misnomer btw since it's really the parent-child index) into a onelevel and sublevel index.

Moreover if we apply the scope to the 'ou' index, we may see that we
have only 10 java coders under the c=US,dc=acme,dc=com branch, instead
of 10000 (not likely, but who knows ? :)

So the idea we had was to use the hierarchy index to add some
information about the other index. Here, we may have the number of java
coder in the c=US,dc=acme,dc=com branch stored under the hierarchy index
for the key 'c=US,dc=acme,dc=com'. We store all the counst for each
index into this Hierarcy index.
As it will be modified when we modify the other index, this might cost a
bit on modifications, deletions and additions, but this will have a huge
impact on the search requests, which is what we target.

In our example, if we suppose that US has only 10 java coders, the
annotated filter will be :

assuming that we also have 200 engineering in the branch, and that the
scope will bring 500 entries.

Now, we will just bring back 10 candidates from the backend instead of 1000.

This is really a gross example, but I think it gives the idea.

Is it totally insane, or does it makes some sense ?

Let me rephrase in my own words to see if I understand the idea. You're suggesting the use of a kind of a scope based LUT or separate index used to return candidates matched by an assertion with a specific attribute and value limited by scope.

Effectively we're going to have this (I think - please correct me) with the two separate system indices for hierarchical relationships instead of just having one parent-child index as we do now. If you look at the documentation here you'll see a description of the onelevel and sublevel indices:

"The one level index maps parent entry identifiers from the master to
the identifiers of their children. This index is used to facilitate
various name space operations like renaming, and moving branches which
impacts children. It is also used by the search engine to conduct one
level search requests."

This index maps ancestor entry identifiers from the master to the
identifiers of all their descendants including immediate children. It
does not map the descendants of the context entry (at the root) of the
partition. This is just unnecessary since all other entries in the
partition satisfy this condition. If this is something we desire to
enumerate we can get a reverse Cursor on the ndn index and advance past
the first entry, to start enumerating all the descendant identifiers of
the context entry.

This index plays a critical role in subtree search. It allows the
search optimizer to detect a count and annotate the modified search
filter for subtree scope nodes. It also allows a Cursor to enumerate
the set of descendants associated with an entry. Without this index,
the search engine must resort to expensive DN based operations for
subtree scope constraint checking."

======== From Doco =======

Now with these two indices as opposed to the one we had we can better constrain subtree search. The subtree search will limit the candidates as will the assertions in the filter as it was given by the user.

But I think you mean more and I think I am catching on to it. You want to constrain individual assertions off an index with scope at each level rather than at just the top perhaps. I have not thought about this at all so this is a good time to explore it. Here's what the search engine does to introduce scope into the AST:

So what would taking the conjunction ('AND' or intersection) of the scope node with each leaf assertion do to influence the search plan and cost of searching instead of taking the conjunction only at the top?

I guess it depends on the kind of logic in the filter. If we have a disjunction (OR) then applying the scope constraint to all child sub-expressions could seriously reduce the IO/processing of search operations while doing the same work. Take this example:

(| (ou=engineering)[100] (c=US)[1000] (l=Jacksonville)[10])

=> 1110 worst case for entire filter

If under scope constraints these numbers are reduced by a factor of 10:

(| (ou=engineering)[10] (c=US)[100] (l=Jacksonville)[1])

=> 111 worst case for entire filter

That's 10x better. So I guess pushing down the scope constraint deep down into the AST is the best option instead of applying it high up. This is how I would implement this idea.